SOLUTION: Sherrie invested some money at 14% interest. Sherrie also invested $186 more than 2 times that amount at 10%. How much is invested at each rate if Sherrie receives $967.20 in in

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Sherrie invested some money at 14% interest. Sherrie also invested $186 more than 2 times that amount at 10%. How much is invested at each rate if Sherrie receives $967.20 in in      Log On

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Question 1134217: Sherrie invested some money at 14% interest. Sherrie also invested $186
more than 2 times that amount at 10%. How much is invested at each rate if Sherrie receives $967.20
in interest after one year? (Round to two decimal places if necessary.)

$----- amount invested at 14%
$---- amount invested at 10%

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
For simple interest:
+I%5B1%5D+=+P%5B1%5D%2Ar%5B1%5D%2A1+
+I%5B2%5D=+P%5B2%5D%2Ar%5B2%5D%2A1+
----------------------------
+I%5B2%5D+=+967.2+-+I%5B1%5D+
+P%5B2%5D+=+2%2AP%5B1%5D+%2B+186+
+r%5B1%5D+=+.14+
+r%5B2%5D+=+.1+
----------------------------
+I%5B1%5D+=+P%5B1%5D%2A.14%2A1+
(1) +I%5B1%5D+=+.14%2AP%5B1%5D+
and
+967.2+-+I%5B1%5D+=+%28+2%2AP%5B1%5D+%2B+186+%29%2A.1%2A1+
+967.2+-+I%5B1%5D+=+.2P%5B1%5D+%2B+18.6+
(2) +-I%5B1%5D+=+.2P%5B1%5D+-+948.6+
Add (1) and (2)
+0+=+.2P%5B1%5D+%2B+.14P%5B1%5D+-+948.6+
+.34P%5B1%5D+=+948.6+
+P%5B1%5D+=+2790+
and
(1) +I%5B1%5D+=+.14%2A2790+
(1) +I%5B1%5D+=+390.6+
and
+I%5B2%5D+=+967.2+-+I%5B1%5D+
+I%5B2%5D+=+967.2+-+390.6+
+I%5B2%5D+=+576.6+
and
+P%5B2%5D+=+2%2AP%5B1%5D+%2B+186+
+P%5B2%5D+=+2%2A2790+%2B+186+
+P%5B2%5D+=+5766+
--------------------------------
$2,790 invested @ 14%
$5,766 invested @ 10%
--------------------------------
check:
+I%5B1%5D+=+P%5B1%5D%2Ar%5B1%5D%2A1+
+390.6+=+2790%2A.14+
+390.6+=+390.6+
OK
+I%5B2%5D=+P%5B2%5D%2Ar%5B2%5D%2A1+
+576.6+=+5766%2A.1+
+576.6+=+576.6+
OK